I’m 20 years old and have stuttered all my life too. I started to stutter on my name towards the end of highschool after one of my coaches joked about the tone I was pronouncing it with lol. In my opinion, with these kinds of cases, the stutter comes from more of a mental block than the actual stuttering part of your brain, because like you, I can say my name fluently in certain situations (ex: I can introduce myself at a party just fine, but I always stutter on my name at work). What helps me in these “mental block” cases is to do everything I can to not let the anxiety take over, and I try to give myself confidence that I will be able to say my name fluently. I think making yourself less anxious and not anticipating the stutter helps in these situations because this certain kind of stutter is caused by the preconceived anxiety that you will stutter. I hope this makes some sort of sense and helps you in some way, but I know everyone’s brains work differently so what works for me may not work for you!